Let `P` be a point on the hyperbola `x^2-y^2=a^2,` where `a` is a parameter, such that `P` is nearest to the line `y=2xdot` Find the locus of `Pdot`

Explanation

To find the locus of the point \( P \) on the hyperbola defined by the equation \( x^2 - y^2 = a^2 \) that is nearest to the line \( y = 2x \), we can follow these steps:

### Step 1: Understand the Hyperbola
The given hyperbola is \( x^2 - y^2 = a^2 \). This can be rewritten in standard form as:
\[ \frac{x^2}{a^2} - \frac{y^2}{a^2} = 1 \]
This indicates that the hyperbola opens along the x-axis.
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